As a test, I've just installed Ubuntu Desktop 22.04.3 LTS on Fusion 13.5 / 2014 Mac mini / Monterey 12.7.1. I chose not to use Easy Install (I've found that to be wonky and not of much value).
I double checked Security & Privacy settings on my Mac. Under Accessibility, VMware Fusion.app is allowed to control my computer - that absolutely needs to be enabled for Fusion to work properly. That begs the question: why isn't the guest picking up the mouse?
Copy and paste of text works properly both ways (host -> guest and guest -> host). Drag and drop does not work with a Wayland session, but does with an Xorg (X11 session).
You say that you've tried installing/reinstalling open-vm-tools and open-vm-tools desktop. Did you check to see if the old-style VMware Tools are installed (they shouldn't be)...
Also is 3D acceleration enabled? If so, is the shared graphics memory in the Display setting of the VM set to 8192 (the recommended value).
This is a strange one. Definitely need more info on the version of Ubuntu that you're running. Perhaps also a look at the vmware.log and mksSandbox.log files would yield some clues about what's going on. (zip them up and post them if you could).